The present invention relates to an aberration correction method and an aberration correction apparatus. More particularly, the present invention relates to a method of and apparatus for correcting aberrations of an optical system for recording a hologram at the stage of reconstructing it. More specifically, the present invention relates to a method of and apparatus for flexibly correcting the spherical aberration, defocusing, etc. of an electron lens, for example, at the stage of reconstructing an image of an electron beam hologram, thereby improving the resolution of the electron microscope including the electron lens. Further, the present invention relates to recovery of an out-of-focus photograph and an electron microscope image affected by aberrations of an electron lens.
Electron beam holography, devised to correct aberrations of an electron lens and to thereby improve the resolution of an electron microscope, comprises two processes, that is, photographic recording of an electron beam hologram, which is effected by using an electron beam, and reconstruction of an electron beam hologram, which is performed by using a laser beam. FIG. 5 shows schematically an electron optical system for photographically recording an electron beam hologram. With a sample 72 disposed at one side of an optical axis, a plane electron wave 71 of high coherence is made incident along the optical axis. The electron wave 71 splits into two components, that is, an object wave that is transmitted and modulated by the sample 72, and a reference wave that does not pass through the sample 72, which are once condensed through an objective electron lens 73 to form an image on an intermediate image plane 75. In this system, an electron biprism 74 is disposed in between the objective lens 73 and the imagery plane 75 to bend the object wave traveling at one side of the central filament of the electron biprism 74 and the reference wave traveling at the other side so that these two waves intersect the optical axis and are superposed one upon the other on the imagery plane 75, thereby forming interference fringes. The interference fringes are enlarged through an electron lens 76 and recorded on a photographic film 77, thereby producing a hologram 77.
The hologram produced in this way contains the record of the amplitude and phase of the object wave spatially enlarged by the electron lens as the contrast and displacement, respectively, of the interference fringes. Unlike optical lenses, electron lenses are all convex lenses, in general. Therefore, with electron lenses, aberrations cannot be canceled by combining together convex and concave lenses. Accordingly, an image that is enlarged by an electron lens is affected by the aberrations of the lens, so that the contrast of the image does not exactly reflect the distribution of the sample. In addition, the resolution is limited to a substantial degree.
However, if an interference pattern, which is produced by superposing the object and reference waves so as to interfere with each other, as described above, is recorded, the object wave affected by the aberrations appears as a wavefront of light at the stage of reconstruction of an image, and it is therefore possible to correct the aberrations.
As one of such methods of correcting aberrations, there has been a method wherein an aberration of an electron lens is corrected by using an aberration of an optical concave lens (A. Tonomura, T. Matsuda and J. Endo, "Spherical Aberration Correction of an Electron lens by Holography", Jpn. J. Appl. Phys. 18 (1979) 1373). In this case, when a parallel beam of light from a laser is applied to an electron beam hologram, the incident light is diffracted by the interference fringes of the hologram, so that the reconstructed wave of the object wave and the conjugate wave appear as two rays of diffracted light generated at both sides of the transmitted wave. Aberration correction may be made either by correcting the reconstructed wave, affected by an aberration of an electron convex lens, by using an optical concave lens, or by correcting the conjugate wave, given an aberration of the opposite sign, by using an optical convex lens.
The aberration correction method employing an optical lens enables aberration correction of high accuracy in theory, but it suffers from the following problems in practical application:
(1) It takes a great deal of time to design and produce an optical lens used for aberration correction. PA1 (2) Since parameters of a lens once produced cannot be changed, the prior art is inferior in terms of applicability. In particular, in the case of an electron beam hologram, the aberration function which is to be corrected varies according to experimental conditions, for example, focusing. Therefore, it is desirable that parameters of an optical element for correction should be flexibly changeable in accordance with experimental conditions. It is desirable, depending on the situation, to make active correction by evaluating the corrected image and feeding back the results of the evaluation. PA1 (3) It is difficult to generate a desired unsymmetrical aberration, e.g., astigmatism, by using an optical lens. PA1 (1) It takes a great deal of labor and time to produce a holographic filter. PA1 (2) Since the correction function coded in the holographic filter cannot be changed, the method is inferior in applicability. PA1 (3) Since a hologram is used for the filter, the corrected image is obtained in the form of diffracted light from the hologram. Therefore, the efficiency of utilization of light lowers.
In the meantime, correction of an out-of focus photograph or an electron microscope image affected by the aberrations of an electron lens has heretofore been made by applying a parallel beam of light to such an out-of-focus photograph while effecting filtering on the Fourier transform plane by using an inverse filter, which is proportional to the reciprocal of the optical transfer function of the optical system. However, since this inverse filter is generally a complex amplitude filter, the production thereof is difficult. In a prior art, such an inverse filter is realized by laying a real-number filter and a holographic filter one on top of the other (G. W. Stroke and M. Halioua, "Image Improvement in High-Resolution Electron Microscopy with Coherent Illumination (Low-Contrast Objects) Using Holographic Image-Deblurring Deconvolution I", Optik 35 (1972) 50).
However, this method involves the following problems: